Green’s Dictionary of Slang

sheeny v.

[neg. Jewish stereotypes: meanness, money obsession; but sense 2. poss. refers to the ‘Jewish’ trade of tailoring rather than the amssing of money]

1. (Aus.) to cheat, to overcharge.

[Aus]Truth (Sydney) 11 Feb. 1/3: I think my last cable ingenious, / I thought it was likely to Sheeny us.

2. (US) to save money by performing small jobs .

C. Fowler letter 28 June in Tomlinson Rocky Mountain Sailor (1998) 131: They can order Americans around in the American Navy, can make lots of money to salt down by doing tailoring —’sheenying’ we call it—or other odd jobs.